Studying the in-medium $φ$ meson spectrum through kaons in proton-nucleus reactions

TL;DR

The paper investigates in-medium mass modifications of the φ meson in proton-nucleus collisions at 30 GeV to illuminate the behavior of the strange-quark condensate and partial chiral symmetry restoration. It employs the off-shell Budapest BUU (BuBUU) transport framework to simulate φ production and decay, focusing on the hadronic decay channel φ → K^+K^- and comparing with the dilepton channel as a cross-check. A key finding is that kaon final-state interactions and threshold effects complicate the kaon-channel signal, whereas a modest, density-dependent mass shift Δm(ρ) tends to enhance the low-mass side of the spectrum. The authors advocate a combined analysis of kaon and dilepton channels, along with target-size and kinematic cuts, to constrain the φ in-medium mass shift, and note that lower beam energies and future facilities could improve sensitivity.

Abstract

Exploring the mass modifications of $φ$ mesons in nuclei provides insights into the nature of strongly interacting matter. Specifically, $φ$ meson mass shifts can be related to the in-medium modification of the strange quark condensate. Therefore, the partial restoration of chiral symmetry can be studied by observing the mass shifts through the decay channels $φ\rightarrow e^+e^-$, and $φ\rightarrow K^+K^-$. In this paper, we examine the possibility of observing the $φ$ meson mass modifications of the $φ$ mesons in 30 GeV proton-nucleus (C, Cu, Pb) collisions, to be studied at the J-PARC E88 experiment, through the kaonic decay channel, with the off-shell Budapest Boltzmann-Uehling-Uhlenbeck (BuBUU) transport model. By applying different mean fields to the kaons, we examine their effects on the invariant mass spectra. Our simulations suggest that, although different mean fields for the kaons do affect the spectrum, there is a common observable effect primarily driven by the $φ$ mass shift. However, due to the threshold associated with the two kaons, the signal we observe is quite different from the one expected in dilepton spectra. Therefore, to meaningfully constrain the mass shift, it will be useful to include both kaon and dilepton channels in the analysis of the experimental data.

Figures (10)

• Figure 1: Comparison of the density and momentum dependence of the (M3) and (M4) mean fields. The dashed lines show the results for the (M4), while the solid lines correspond to the (M3) potentials. Here, $n=\rho/\rho_0$ is the normalized density, where $\rho_0=0.168$ [fm$^{-3}$].
• Figure 2: Comparison of the invariant mass spectra of kaon pairs in p+Cu reactions at 30 GeV bombarding energies with different kaonic mean fields without final state interactions of kaons.
• Figure 3: Effects of the scatterings and absorption of kaons on the invariant mass spectrum when applying the (M3) mean field in p+Cu collisions at 30 GeV.
• Figure 4: Comparison of the (M3), and (M4) mean fields at C, Cu, and Pb targets, including all of the considered final state interactions of the kaons.
• Figure 5: Invariant mass spectra of K meson pairs without mass modifications of the $\phi$ mesons for C, Cu, and Pb targets in proton induced reactions at $30$ GeV bombarding energies by using the (M3) mean fields.